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A101334 n^n - (n+1)^(n-1). 5
0, 0, 1, 11, 131, 1829, 29849, 561399, 11994247, 287420489, 7642052309, 223394306387, 7123940054219, 246181194216957, 9165811757198641, 365836296342931439, 15584321022199735823, 705800730789742512401, 33866021217511735389485, 1716275655660313589123979 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

b(n) = n^n mod (n+1)^(n-1)  begins: 0, 0, 1, 11, 6, 533, 13042, 37111, 2428309, ...

a(n) is the number of functions f:{1,2,...,n}->{1,2,...,n} with at least one cycle of length >= 2. - Geoffrey Critzer, Jan 11 2013

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..150

FORMULA

E.g.f.: 1/(1-T(x)) - exp(T(x)) where T(x) is the e.g.f. for A000169. - Geoffrey Critzer, Jan 11 2013

a(n) = Sum_{k>0} A264902(n,k). - Alois P. Heinz, Nov 29 2015

EXAMPLE

a(3) = 3^3 - 4^2 = 27-16 = 11.

MATHEMATICA

ReplacePart[Table[n^n-(n+1)^(n-1), {n, 0, nn}], 0, 1]  (* Geoffrey Critzer, Jan 11 2013 *)

PROG

(PARI) for(x=1, 20, print( x^x-(x+1)^(x-1) ))

(Python)

for n in range(33):

  print n**n - (n+1)**(n-1),

CROSSREFS

Cf. A046065, A264902.

Sequence in context: A075509 A061113 A261689 * A222872 A068645 A097258

Adjacent sequences:  A101331 A101332 A101333 * A101335 A101336 A101337

KEYWORD

nonn

AUTHOR

Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 24 2004

EXTENSIONS

a(0), Python program and b(n) in comments added by Alex Ratushnyak, Aug 06 2012

STATUS

approved

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Last modified December 10 23:07 EST 2016. Contains 279021 sequences.